Question

The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The accompanying data table gives the value and the annual revenue for 15 major sport teams. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Complete parts​ (a) through​ (e) below.

a. Construct a scatter plot. (Already Answered)

b. Use the​ least-squares method to determine the regression coefficients

b0	=	_____
b1	=	_____
		​(Round to two decimal places as​ needed.)

c. Interpret the meaning of b0 and b1 in this problem. Choose the correct answer below.

A.The​ Y-intercept, b0​, implies when the annual revenue is​ zero, the franchise value is b0​,in millions dollars. The​ slope,b1​,implies the revenue is equal b1​, in millions of dollars.

B.The​ Y-intercept,b0​,implies that if the annual revenue is​ zero, the franchise value is equal to the value of b0​,in millions of dollars. The​ slope,b1​,implies that the average franchise value is equal to b1​,in millions of dollars.

C.An interpretation of the​ Y-intercept,b0​,is not meaningful because no sports franchise is going to have a revenue of zero. The​ slope,b1​,implies that for each increase of 1 million dollars in annual​ revenue, the franchise value is expected to increase by b1​,in millions of dollars.

D.The​ Y-intercept,b0​,implies that if the annual revenue is​ zero, the franchise value is equal to b0​,in millions of dollars. The​ slope,b1​,implies that for each increase of 1 million dollars in annual​ revenue, the franchise value is expected to decrease by b1​,in millions of dollars.

d. Predict the mean franchise value​ (in millions of​ dollars) of a sports team that generates​$200 million of annual revenue.

Yi=$_______million ​(Round to the nearest integer as​ needed.)

e. What would you tell a group considering an investment in a major sports team about the relationship between revenue and the value of a​ team?

A.The value of the franchise is not affected by the changes in revenue.

B.The value of the franchise can be expected to decrease as revenue increases.

C.The value of the franchise can be expected to increase as revenue decreases.

D.The value of the franchise can be expected to increase as revenue increases.

Data Table

Annual_Revenue_(millions_of_dollars)	Franchise_Value_(millions_of_dollars)
264	787
166	207
214	447
194	406
193	380
186	463
232	516
191	468
238	675
231	676
277	860
251	614
192	503
218	457
220	626

Answer 1

a )

b )

Find X⋅Y and X2 as it was done in the table below.

X	Y	X⋅Y	X⋅X
264	787	207768	69696
166	207	34362	27556
214	447	95658	45796
194	406	78764	37636
193	380	73340	37249
186	463	86118	34596
232	516	119712	53824
191	468	89388	36481
238	675	160650	56644
231	676	156156	53361
277	860	238220	76729
251	614	154114	63001
192	503	96576	36864
218	457	99626	47524
220	626	137720	48400

b₀ = -522.18, b₁ = 4.87

c )

The​ Y-intercept,b0​,implies that if the annual revenue is​zero, the franchise value is equal to b0​,in millions of dollars. The​ slope,b1​,implies that for each increase of 1 million dollars in annual​ revenue, the franchise value is expected to increase by b1​,in millions of dollars.

d ) x = 200

y = -522.18 + 4.87 ( 200 )

= 451.82

= 452

e )  The value of the franchise can be expected to increase as revenue increases.